The ratio of thermal conductivities of two rods of different materials is $5 : 4$ . The two rods have the same area of cross-section and the same thermal resistance. They will have the lengths in the ratio

4 : 5

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9 : 1

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1 : 9

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5 : 4

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Solution

The correct option is D $5 : 4$
Given $A_{1} = A_{2}$ and $\frac{K_{1}}{K_{2}} = \frac{5}{4}$
$∴ R_{1} = R_{2} ⟹ \frac{l_{1}}{K_{1} A_{1}} = \frac{l_{2}}{K_{2} A_{2}} ⟹ \frac{l_{1}}{l_{2}} = \frac{K_{1}}{K_{2}} = \frac{5}{4}$

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The ratio of thermal conductivities of two rods of different materials is 5:4. The two rods have the same area of cross-section and the same thermal resistance. They will have the lengths in the ratio

The correct option is D 5:4Given A1=A2 and K1K2=54∴R1=R2⟹l1K1A1=l2K2A2⟹l1l2=K1K2=54

The ratio of thermal conductivities of two rods of different materials is $5 : 4$ . The two rods have the same area of cross-section and the same thermal resistance. They will have the lengths in the ratio

The correct option is D $5 : 4$
Given $A_{1} = A_{2}$ and $\frac{K_{1}}{K_{2}} = \frac{5}{4}$
$∴ R_{1} = R_{2} ⟹ \frac{l_{1}}{K_{1} A_{1}} = \frac{l_{2}}{K_{2} A_{2}} ⟹ \frac{l_{1}}{l_{2}} = \frac{K_{1}}{K_{2}} = \frac{5}{4}$